Petersen Graph Decompositions of Complete Multipartite Graphs

摘要

Let P be the Petersen graph, and K _u(h) the complete multipartite graph with u parts of size h. A decomposition of K _u(h) into edge-disjoint copies of the Petersen graph P is called a P-decomposition of K _u(h) or a P-group divisible design of type h u . In this paper, we show that there exists a P-decomposition of K _u(h) if and only if , , and u ≥ 3 with a definite exception (h, u) = (1, 10).